Willful Ignorance: The Mismeasure of Uncertainty

CHAPTER 4 HARDLY TOUCHED UPON

In the 1680s, leading mathematicians were preoccupied mainly with the new infinitesimal calculus originated by Isaac Newton and Gottfried Leibniz. The mathematics of chance was at the periphery of attention, and Huygens's little treatise was just about all that existed on the subject. After its publication in 1657, it rode the coattails of van Schooten's popular textbook all over Europe, and became a standard in its own right. Over the course of the next 50 years, it was virtually unique as a reference on the calculus of chance. During this period, there was little advancement of Huygens's ideas, with one notable exception. Jacob Bernoulli was the only person to progress substantially beyond his French and Dutch predecessors in developing the mathematics of chance.

Regrettably, Bernoulli chose not to publicize his work, and was eventually overtaken by illness and death. So his technical and philosophical achievements were not revealed until much later. Pierre Raymond de Montmort (1678–1719), learned of Jacob Benoulli's efforts from several eulogies given after his death in 1705. Based on this limited information, Montmort successfully undertook to extend Huygens's results.¹ His groundbreaking Essay D'Analyse sur les Jeux de Hazard (Analytic Essay on Games of Chance) was published in 1708. In an “advertisement” for the second edition in 1713, just as Bernoulli's work was finally destined to see the light of day, Montmort explained that the mathematics ...